The packaging of genomic information and the regulation of gene expression are both fundamentally important to eukaryotic life. Meters of human DNA must fit inside the micron-diameter nucleus while still rapidly becoming available for templated processes such as transcription, replication, and repair. Therefore, the DNA-protein complex known as chromatin must dynamically transition between more compact, closed states and more accessible, open ones. To fully understand chromatin structure and dynamics, it is necessary to employ a multifaceted approach, integrating different general philosophies and scientific techniques that include experiment and computation. Since the DNA in chromatin is organized into arrays of nucleosomes, we take a bottom-up approach in this dissertation, striving first to understand the structure and dynamics of an individual nucleosome and subdomains thereof. Atomistic computational methods have provided useful tools to study DNA and protein dynamics at the nanosecond, and recently microsecond, timescale. In this dissertation, we present recent developments in the understanding of the nucleosome though atomistic molecular dynamics (MD) simulations. By applying different all-atom MD computational techniques, we demonstrate that replacing the canonical H3 histone with the centromere-specific variant CENP-A translates to greater structural flexibility in the nucleosome, that replacing H3 with CENP-A increases the plasticity of an individual histone dimer, and that the effects of acetylation on the H4 histone tail are cumulative and specific to lysine 16 mono-acetylation.